Process prediction and control is crucial to optimizing the outcome of complex multi-step production processes. For example, the production process for integrated circuits comprises hundreds of process steps (i.e., sub-processes). Each process step, in turn, may have several controllable parameters, or inputs, that affect the outcome of the process step, subsequent process steps, and/or the process as a whole. In addition, the impact of the controllable parameters and maintenance actions on the process outcome may vary from process run to process run, day to day, or hour to hour. The typical integrated circuit fabrication process thus has a thousand or more controllable inputs, any number of which may be cross-correlated and have a time varying, nonlinear relationship with the process outcome. As a result, process prediction and control is crucial to optimizing process parameters and to obtaining, or maintaining, acceptable outcomes.
Regression techniques have been used to model relationships between various process variables and characteristics of the process output (e.g., the quality, according to at least one metric of interest, of a finished product). The use of neural networks has facilitated successful modeling of processes having large numbers of variables whose interrelationship and contribution to the output metric of interest cannot easily be described.
Run-to-run controllers typically base analysis of the controlled process on metric values from a single output piece or a single lot of pieces, such as semiconductor wafers. A risk or cost function may be used to evaluate a set of metric values, permitting the process controller to reduce the risk associated with each wafer. The level of risk may be determined on a variable-by-variable basis and quantified, e.g., on a scale of 0 to 10.
Complex processes such as semiconductor manufacture, however, depend heavily on process and maintenance history. Such environments involve multivariable processes and production equipment vulnerable to gradual degradation but amenable to numerous different preventive maintenance procedures. As the system ages, it can be difficult to determine where to focus maintenance attention and resources. For example, it is often difficult to deduce from small, wafer-to-wafer changes that a particular maintenance action is urgently needed. To obtain a multivariate metric of the urgency of various corrective actions, it is desirable to place analysis of system variables in a time domain, rather than, for example, isolating an individual wafer from the process history.
For a process or system variable, the risk is higher the further the measured value diverges from a target metric for the variable. For some variables that represent the age of a part or the time since a particular maintenance activity was performed on a controlled tool, a decreasing risk may be assigned for a part or maintenance action as the time since the last maintenance activity was performed due to amortization of the initial cost of the part and/or labor to perform the action.